Simplify the following expression: $p = \dfrac{-2k^2 + 12k - 10}{k - 1} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ p =\dfrac{-2(k^2 - 6k + 5)}{k - 1} $ Then we factor the remaining polynomial: $k^2 {-6}k + {5} $ ${-1} {-5} = {-6}$ ${-1} \times {-5} = {5}$ $ (k {-1}) (k {-5}) $ This gives us a factored expression: $\dfrac{-2(k {-1}) (k {-5})}{k - 1}$ We can divide the numerator and denominator by $(k + 1)$ on condition that $k \neq 1$ Therefore $p = -2(k - 5); k \neq 1$